Frequency-dividing circuit for signals of sawtooth waveform

ABSTRACT

A frequency-dividing circuit for signals of sawtooth waveform, comprising: a buffer transistor to the base of which an input sawtooth wave and an output square wave of a square-wave frequency divider are applied in their states of equal peak amplitude through mixing resistors having equal value, and a mixing circuit for obtaining an output of a frequency-divided sawtooth wave from the emitter of said buffer transistor, a compensating DC voltage being superposed at any point of the circuit so that the lower ends of the mixed signal appearing at said base are offset from said emitter potential by a voltage value which is greater than the forward voltage drop between the base and the emitter of the transistor thereby to cause said buffer transistor to perform a perfect class &#39;&#39;&#39;&#39;A&#39;&#39;&#39;&#39; amplifying operation. Furthermore, modifications of the circuits mentioned above are described.

United States Patent [72] Inventor Yasuji Uchiyama Hamakita, Japan [21]Appl. No. 10,195 [22] Filed Feb. 10, 1970 [45] Patented Dec. 14, 1971[73] Assignee Nippon Gakki Seizo Kabushikl, Kalsha Ilamanatsu-shi,Shizuoka-ken, Japan [32] Priorities Feb. 13, 1969 [33] Japan [31]44/108;

Feb. 13, 1969, Japan, No. 44/111867; Feb. 13, 1969, Japan, No. 44/111868[54] FREQUENCY-DIVIDING CIRCUIT FOR SIGNALS 0F SAWTOOTH WAVEFORM 10Claims, 22 Drawing Figs.

[52] 11.8. C1 307/225, 307/228, 307/271, 328/36, 328/39. 328/157,328/181, 328/184, 330/147 [51] Int. Cl ..H03k 21/00 [50] Field of Search307/220, 225, 228,271; 328/30, 36, 39, 157, 158, 181, 184, 185; 330/147[56] References Cited UNITED STATES PATENTS 2,589,807 3/1952 Higinbotham328/185 X Primary E.raminer-Stanley T. Krawczewicz AnorneyHolman & SternABSTRACT: A frequency-dividing circuit for signals of sawtooth waveform,comprising: a buffer transistor to the base of which an input sawtoothwave and an output square wave of asquare-wave frequency divider areapplied in their states of equal peak amplitude through mixing resistorshaving equal value, and a mixing circuit for obtaining an output of afrequency-divided sawtooth wave from the emitter of said buffertransistor, a compensating DC voltage being superposed at any point ofthe circuit so that the lower ends of the mixed signal appearing at saidbase are offset from said emitter potential by a voltage value which isgreater than the forward voltage drop between the base and the emitterof the transistor thereby to cause said buffer transistor to perform aperfect class A" amplifying operation. Furthermore. modifications of thecircuits mentioned above are described.

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5 Sheets-She t 1 INVIEN'IUR Ym sun UCHI m ATTORNEYS Patented Dec. 14,1971 5 Shc0ts-$heet 3 W G F FIG MM 1 FIG. 2(a) YWSMW Mali-r WW MATTORNEYS Patented Dec. 14, 1971 5 Sheets-Sheet 5 ATTORNEY$FREQUENCY-DIVIDING CIRCUIT FOR SIGNALS OF SAWTOOTH WAVEFORM BACKGROUNDOF THE INVENTION The present invention relates to a frequency-dividingcircuit for signals of sawtooth waveform in which a frequency-dividedsawtooth wave can be obtained by mixing a square wave and a sawtoothwave, and more particularly relates to frequencydividing circuits forsignals of sawtooth waveform, which can be connected in cascade from apoint of view of direct current.

Hitherto, a frequency-dividing circuit constructed by connecting aplurality of flip-flop circuits or a plurality of blocking oscillatorsin cascade has been conventionally used as a frequency divider for usein electronic musical instruments. However, the conventional frequencydividers mentioned above have various disadvantages as well as variousadvantages. That is, since the frequency divider utilizing flip-flopcircuits can carry out frequency-dividing operation within a broadfrequency range having no limitation, it is very easy to manufacturesaid frequency divider in the case when a plurality of the frequencydividers are to be used, but since their out put waves are of squareform and contain only harmonic frequencies of odd order withoutcontaining harmonic frequencies of even order, said output waves areincomplete for practical use as a sound source in electronic musicalinstruments.

On the other hand, an output wave of a frequency divider comprisingcascaded blocking oscillator circuits is of sawtooth waveform, so thatsaid output wave has all of harmonic components, thus causing favorableproduction of timbres of any musical instrument, which means that saidfrequency divider is ideal as the sound source. However, the blockingoscillator circuit itself is liable to produce a self-runningoscillation of a particular frequency in the case when any synchronizingmeans is not applied thereto, that is, said circuit includes therein atime-constant circuit the time constant of which is determined by acapacitance, a resistance, characteristics of active elements, biasvoltage, power source voltage, and the like. Accordingly, the blockingoscillator circuit is affected by fluctuation of the above-mentionedvalues of various elements and variation of voltages and temperature,whereby frequency of the free-running oscillation is liable to bevaried. Furthermore, when the blocking oscillator circuit is used asone-half frequency divider by applying synchronization thereto,frequency of the input synchronous signal is required to be higher thandouble value and lower than triple value of its free-running oscillationfrequency, so that its operating frequency is limited. Accordingly, forthe purpose of obtaining a desired operation frequency, values of thecircuit elements such as capacitors and resistors should be selected tobe matched with said desired frequency, and in the case of using thefrequency divider as a sound source circuit of any musical instrument,elements of the circuit should be individually designed so as to bemutually different from elements of other circuits in order to coverfrequency range over several octaves, thus causing difficulty ofmanufacture of the circuits. Furthermore, as sound frequency approachesbass region, larger time constant is required. In this case, capacitorof a larger capacitance is required, thus causing higher cost andbulkiness of the circuit.

SUMMARY OF THE INVENTION It is an essential object of the invention toprovide a frequency-dividing circuit for signals of sawtooth waveformhaving no such disadvantages of the conventional frequencydividingcircuits as mentioned above, and more particularly to provide afrequency divider favorably adapted to produce a sound source for anyelectronic musical instrument.

It is another object of the invention to provide a frequencydividingcircuit for signals of sawtooth waveform, which produces afrequency-divided sawtooth wave by mixing a square wave from asquare-wave frequency-dividing circuit and a sawtooth wave at a mixingcircuit, disposing large amplitude signals without distortion.

It is a further object of the invention to provide frequencydividingcircuits for signals of sawtooth waveform, which can be connected incascade to each other from a point of view of direct current, and aresimple in their construction.

It is a further object of the invention to provide frequencydividingcircuits for signals of sawtooth waveform which can be easily connectedin cascade without using DC blocking capacitor and bias resistor of thetransistor.

It is still a further object of the invention to provide afrequency-dividing circuit for signals of sawtooth waveform, saidcircuit being more particularly adapted for various integrated circuitsof any electronic musical instrument.

The foregoing and other objects of the invention have been attained by afrequency-dividing circuit comprising a buffer transistor to the base ofwhich an input sawtooth wave and an output square wave of a square-wave:frequency divider are applied in their states of equal peak amplitudethrough mixing resistors having equal value; and a mixing circuit forobtaining an output of a frequency-divided sawtooth wave from theemitter of said buffer transistor, characterized in that a means isprovided for causing superposition of a compensating DC voltage at anyportion of the circuit in such a manner that the lower ends of the mixedsignal appearing at the base is offset from the emitter potential by avoltage value sufficient to compensate a base-to-emitter forward voltagewhich means the forward voltage drop between the base and the emitter,thereby causing said buffer transistor to perform a perfect class A"amplifying operation.

The features and function of the invention will become more apparent andmore readily understandable by the following description and theappended claims when read in connection with the accompanying drawings,in which same or equivalent members are designated by the same numeralsand characters.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a circuit connection diagramshowing an embodiment of the invention;

FIGS. 2(a) to 20) are waveform diagrams showing the signal relationshipsin the circuit shown in FIG. 1;

FIG. 3 is a circuit connection diagram showing a second embodiment ofthe invention;

FIGS. 4(a) to 40) are waveform diagrams showing the signal relationshipsin the circuit shown in FIG. 3;

FIG. 5 is a circuit connection diagram showing a third embodiment of theinvention;

FIGS. 6(a) to 6(d) are waveform diagrams showing the signalrelationships in the circuit shown in FIG. 5;

FIG. 7 is a circuit connection diagram showing a fourth embodiment ofthe invention;

FIG. 8 is a waveform chart illustrating the operation of the circuitshown in FIG. 7;

FIG. 9 is a circuit connection diagram showing a fifth embodiment of theinvention; and

FIGS. 10(a) to 10(d) are waveform diagrams illustrating the signalrelationships in the circuit shown in FIG. 9.

DETAILED DESCRIPTION OF THE INVENTION Referring to FIGS. 1 and 2, asawtooth wave shown in FIG. 2(a) is applied to a square-wavefrequency-dividing circuit 1 comprising transistors Tr, and Tr from itsinput terminal 0 whereby a square wave shown in FIG. 2(b) is derivedfrom output terminal 0,, of said circuit ll. When the transistor Tr, inthe output side of said frequency-dividing circuit 1 is in conductivestate, the output voltage is equal to a saturation voltage of saidtransistor and is nearly zero, but when the transistor Tr is in cutoffstate, the output voltage comes to have a voltage nearly equal to thatof normal source voltage +V and this alternating operation producessquare wave having a considerable large amplitude.

Assuming that the sawtooth wave in FIG. 2(a) from the terminal and thesquare wave from the square-wave frequency-dividing circuit 1 are madesame in their peak amplitudes and mixing resistors R and R of a mixingcircuit 2 comprising a buffer transistor Tr, having a high inputimpedance are set to same value respectively, a sawtooth wave shown inFIG. 2(a) having a frequency of f/2 (1: original frequency) and samepeak amplitude as that of said former waves is obtained at theconnection point M. This output sawtooth wave is applied to the base ofthe buffer transistor Tr, having a high input impedance, whereby anoutput wave is derived from the emitter 0,, of said transistor TrAlthough the emitter of the transistor Tr is connected through anemitter resistor R to the ground, the transistor Tr does not performclass A" amplifying operation below the base-to-emitter forward voltageV which is the nonconducting forward voltage between the base and theemitter, which results in that an imperfect sawtooth wave with its underside shown by a dotted line cut is obtained, as shown in FIG. 2(d). Inthe case when silicon transistor is used as the transistor Tr theabove-mentioned voltage is about 0.6 volt. Even if such afrequency-divided imperfect sawtooth wave is applied to a mixing circuit20 of the succeeding stage, a perfect sawtooth wave can not be obtainedfrom the terminal 0 so that, the above-mentioned frequency-dividingstages cannot be connected in cascade one after another.

Accordingly, in the embodiment of FIG. 1 according to this invention, itis constructed that a resistor Rb is connected between the base andcollector of the transistor Tr and a DC voltage nearly equal to said Vis superposed to the signal brought at the base of the transistor TrThat is, sawtooth wave shown in FIG. 2(e) can be obtained by superposinga direct current component V to sawtooth wave at the connection point M.By such organization, class A" operation of the transistor Tr, can besurely obtained, whereby a perfect output sawtooth wave as shown in FIG.2(e) can be obtained.

Of course, the peak amplitude of the mixed resultant sawtooth wave shownin FIG. 2(2) reduces by a smaller amount than that of each of the twosignals before mixing, because of the load effect of the resistor R,connected between the base and collector of the transistor Tr However,when a source voltage +V for the collector of the transistor T isselected sufficiently high and a value of the resistor Rb is alsoselected sufficiently high, the above-mentioned reduction of the peakamplitude of the mixed resultant sawtooth wave becomes so small that ithas no problem in practical use.

The emitter of the transistor Tr, is connected not only to the outputterminal 0, but also to one input side of the succeeding mixing circuit20, and output square wave at the terminal O is applied not only to themixing circuit 2 as one input thereof, but also to the succeedingsquare-wave frequency-dividing circuit la as a trigger input thereof. Inaddition, output terminal 0,, of the above-mentioned circuit isconnected to the other input side of the mixing circuit 2a. Since themixing circuit is constructed the same as the mixing circuit 2 andbuffer transistor Tr of the mixing circuit 2a performs normally class A"operation, a frequency-divided perfect sawtooth wave can be obtainedfrom the terminal 0 at the output side of the mixing circuit 2a.Furthennore, by connecting in cascade a plurality of frequency-dividingstages, each being composed of a set of square-wave frequency-dividingcircuit (1, 1a...or) and a mixing circuit (2, 2a...), the desiredfrequency-divided sawtooth waves can be easily ob tained from the outputterminal of each frequency-dividing stage.

Referring to the embodiment shown in FIG. 3, a DC voltage is superposedto an input sawtooth wave in response to the number offrequency-dividing stages connected in cascade so as to obtain surelyclass A" operation of buffer transistors in the mixing circuits to beconnected in cascade. When two frequency-dividing stages are connectedin cascade as shown in FIG. 3, a sawtooth wave obtained by superpositionof a pure sawtooth wave and a positive DC voltage corresponding to sixtimes as large as the base-to-emitter forward voltage V between the baseand the emitter of the butter transistor Tr said voltage V correspondingto minimum voltage adapted to operate said transistor, is applied to theinput terminal 0,, as shown in FIG. 4(e). Accordingly, class A"operation of the bufier transistor TrMl is established, thereby afrequency-divided sawtooth wave shown in FIG. 40) can be obtained fromthe emitter of the buffer transistor Tr when a sawtooth wave at theterminal 0 and a square wave from the square-wave frequency-dividingcircuit 1 are mixed in the mixing resistors R and R When thefrequency-divided sawtooth wave thus obtained is applied to one inputterminal of the succeeding mixing circuit 2a and is mixed with a squarewave from the succeeding square-wave frequency-dividing circuit la toproduce a desired frequency-divided sawtooth wave, class A" operation ofthe buffer transistor Tr is similarly established, because the minimumvoltage of the above-mentioned resultant sawtooth wave is larger thanthe voltage V of the buffer transistor Tr whereby a perfectfrequency-divided sawtooth wave can be obtained from the terminal 0,Although the foregoing description relates to the embodiment using twofrequency-dividing stages, class A operation of the buffer transistor ineach frequency-dividing stage can be surely obtained by applying asawtooth wave superposed with a DC voltage 2(2"l )V to the terminal O inthe case when the number of the frequency-dividing stages is n, wherebyperfect sawtooth waves can be obtained from their output terminals,respectively.

Referring to an embodiment shown in FIG. 5, square-wavefrequency-dividing circuit 1 consisting of a flip-flop circuit is causedto operate by a positive source voltage (+V.) and the ground potential.The collector of the buffer transistor Tm] in the mixing circuit 2 isconnected to a positive source voltage (+V and the emitter thereof isconnected through an emitter resistor R to an emitter source voltage(V;,) biased negatively with respect to the ground potential.

Assuming that, in the circuit shown in FIG. 5, a DC voltage (V biasednegatively is superposed to a sawtooth wave at the input terminal 0 asshown in FIG. 6(a) and the resultant sawtooth wave thus obtained ismixed with a square wave shown in FIG. 6(b) and obtained from thesquare-wave frequency-dividing circuit 1 in the mixing resistors R and Rhaving same value respectively, a negative DC voltage superposedsawtooth wave as shown in FIG. 6(a) comes to a value of ,/2 at the baseof the transistor Tr because a mixing loss is one-half. On the otherhand, since a negative DC voltage corresponding to an amount equal tothe voltage V between the base and the emitter of the transistor Tr, issuperposed to the output wave at the emitter (at the output terminal 0,of the transistor Tr the resultant negative DC voltage to be superposedto a frequency-divided sawtooth wave comes to (V /2+V as shown in FIG.6(d).

Therefore, let it be assumed that the negative DC voltage (V superposedto the sawtooth wave at the input terminal O is equal to -2V,,,;, anegative DC voltage superposed to a frequency-divided sawtooth wave atthe output terminal 0,, comes to 2V,; also. That is, the negative DCvoltages superposed to the sawtooth wave come to 2V respectively at boththe input terminal 0 and the output terminal 0 Accordingly, assumingthat the emitter source voltage (V;,) of the buffer transistor Tr, isselected to a value equal to or more negative than the negative DCvoltage 2V,,,; superposed to a frequency-divided sawtooth wave, thebuffer transistor Tr makes sure A" operation, whereby a perfect sawtoothwave can be obtained from the emitter thereof.

Moreover, when the frequency-divided sawtooth wave thus obtained isapplied to the base of the succeeding mixing circuit 2a as one inputthereof and is mixed with a square wave from the succeeding square-wavefrequency-dividing circuit Ia, thereby to derive a sawtooth wave ofwhich frequency is further divided to one-half from the emitter of thebuffer transistor Tr a DC voltage is to be superposed to thefrequency-divided sawtooth wave thus obtained comes to -2V also. Sincethis DC voltage (-2V is equal to the emitter source voltage (V,,) of thebuffer transistor Tr or nearly equal to the ground potential, thesimilar class A" operation can be obtained surely, whereby a perfectsawtooth wave can be obtained from the output terminal Although theforegoing description relates to the embodiment using twofrequency-dividing stages, it is apparent that class A" operation of thebuffer transistors in each frequency-dividing stage can be surelyobtained in the case when one frequency-dividing stage is utilized ormore than three are utilized.

Referring to an embodiment shown in FIG. 7, the circuit is constructedso that the emitter source voltage of the buffer transistor in themixing circuit is biased more negatively than the ground potential. Inthe circuit of FIG. 7, the emitter of the buffer transistor Tr, in themixing circuit 2 is connected through the emitter resistor R to thesource voltage biased more negatively than the ground potential. As willbe apparent from the foregoing description, a frequency-divided sawtoothwave superposed with a DC voltage (-V,,,;) can be obtained at theemitter (at the output terminal 0, of the transistor Tr, and similarlyeach of frequency-divided sawtooth waves, superposed DC voltages I.SVl.75V ,,..respectively, having one-half frequency of the outputfrequency of the preceding frequency-dividing stage can be obtainedsuccessively at the output terminal of each frequency-dividing stage.Herein, assuming that each of the emitter source voltage (--V,,) of thebuffer transistors is selected to be equal to 2V,,,; or more negativethan 2V the buffer transistors in each of the frequency-dividing stagesmake sure class A" operation, thereby perfect sawtooth waves can beobtained at each of the emitters of the buffer transistors as shown inFIG. 8.

Although the foregoing paragraph is described as to the embodimentwherein frequency-dividing stages are connected infinitely, it isapparent that when a number n of the frequencydividing stages are to beconnected in cascade, a DC voltage to be superposed to frequency-dividedsawtooth wave which is obtained from the output terminal of the nthfrequency-dividing stage comes to -2(l- /")V Accordingly, the emittersource voltage of the buffer transistor may be selected to be equal to avalue of 2( l-%")V or more negative than that of-2( 1-%" v,,

Referring to an embodiment shown in FIG. 9, the circuit is constructedso that a DC Voltage biased positively may be superposed to afrequency-divided square wave from a squarewave frequency-dividingcircuit 1 so as to obtain surely class "A" operation of the buffertransistor in each of the mixing circuits connected by the desirednumbers in cascade. In the circuit of FIG. 9, each of the square-wavefrequency-dividing circuits 1 and la is connected between positivesource voltages +V, and +V The output of the above-mentioned square-wavefrequency-dividing circuit 1 is equal to voltage having a valuecorresponding to sum of the source voltage +V and saturation voltage ofthe transistor Tr, when the transistor Tr in the output side of thesquare-wave frequency-dividing circuit I is in conductive state, but itcomes to be nearly equal to the source voltage +V because theabove-mentioned saturation voltage is nearly equal to zero.

Assuming that, in this circuit, such a sawtooth wave at the inputterminal 0 as shown in FIG. (a) and such a square wave from thesquare-wave frequency-dividing circuit ll superposed with a positive DCvoltage +v as shown in FIG. 10(1)) are mixed through the mixingresistors R and R having same value respectively, such afrequency-divided sawtooth wave superposed with a positive DC voltage(+V /2) as shown in FIG. 10(0) can be obtained at the base of thetransistor Tr because a mixing loss is one-half. 0n the other hand,since a negative DC voltage is superposed by the amount equal to thevoltage V between the base and the emitter of the transistor Tr to theoutput wave at the emitter (at the output terminal 0 of the transistorTr the resultant DC voltage superposed to a frequencydivided sawtoothwave comes to (+V /2V, as shown in FIG. 10(d).

Therefore, if the positive DC voltage (+V to be superposed to thefrequency-divided squane wave is selected to be equal to +2V a DCvoltage to be superposed to the frequency-divided sawtooth wave at theoutput terminal 0 comes to zero. That is, the DC voltages to besuperposed to the sawtooth wave come to zero respectively at both theinput terminal O and the output terminal 0 Accordingly, when the sourcevoltage (+V of the square-wave frequencydividing circuit is selected toa value equal to 2V the buffer transistor Tr makes sure class "A"operation, whereby a perfect sawtooth wave can be obtained from theemitter thereof.

Moreover, when the frequency-divided sawtooth wave thus obtained isapplied to the succeeding mixing circuit 20 as one input thereof and ismixed with a square wave obtained from the succeeding square-wavefrequency-dividing circuit la to and superposed with a positive DCvoltage ZV thereby to derive a sawtooth wave of which frequency isfurther divided to one-half from the emitter of the buffer transistor Tra DC voltage to be superposed to the frequency-divided sawtooth wavethus obtained comes to zero. Accordingly, class A operation of thetransistor Tr is surely obtained, whereby a perfect sawtooth wave can beobtained from the output terminal 0,, of the succeeding mixing circuit2a. Furthermore, since there are small fluctuations in voltage V of thetransistors, it is preferable to set a source voltage (+V of thesquare-wave frequency-dividing circuit to a voltage somewhat larger than2V In the above-mentioned embodiment, a common source voltage (+V toeach of the square-wave frequency-dividing circuits is utilized as ameans to superpose a positive DC voltage to frequency-divided squarewave, but it is possible to connect each of the circuits throughresistor or diode and the like to the ground without connecting each ofthe square-wave frequency'dividing circuits to the common source voltage(+V It will be appreciated that by the use of the system according toone of the above-mentioned embodiments of the invention it is possibleto easily obtain a sawtooth wave frequencydividing circuit composed of aplurality of a frequency-dividing stages which can be connected incascade successively and to provide an improved sawtoothfrequency-dividing circuit adapted for sound source of electronicmusical instruments and more particularly adapted for integrated circuitthereof. It will be understood, of course, that these embodiments arepresented only as exemplary to the invention, and many changes andmodifications will become apparent to those skilled in the art.

What we claim is:

1. A circuit for producing signals of sawtooth wave having at least onestage comprising: a buffer transistor; at least two mixing resistors ofequal value feeding at the base of the transistor an input sawtooth waveand a square wave of equal peak amplitude; a frequency mixing circuitincluding said buffer transistor and said resistors to mix the inputsawtooth wave and square wave to produce a required sawtooth signal; asquare-wave frequency-dividing circuit having an output thereofconnected to one of said mixing resistors to feed said square wave intothe frequency-mixing circuit; and means to superpose a DC voltage at aportion of the circuit so as to lower ends of said divided frequencyoutput signal to an extent sufficient to compensate the voltage dropbetween the transistor base and emitter causing said buffer transistorto perform as a perfect class A" amplifier.

2. The circuit as claimed in claim l. which includes an emitter resistorconnected at one end thereof to the emitter of said buffer transistorthe other end being earthed, and a DC voltage superposing resistorconnected between the base and collector of the buffer transistor.

3. The circuit as claimed in claim 1 in which said means to superpose aDC voltage is adapted to superpose the voltage in the same direction asthe starting operational voltage of said buffer transistor.

4. The circuit as claimed in claim 1 in which said means to superpose aDC voltage includes connections to superpose the DC voltage to saidinput sawtooth wave, and means to set the emitter source voltage of saidbuffer transistor to a value at least equal to the DC voltage and to soset the direction of said emitter source voltage that the buffertransistor is conductive.

5. The circuit as claimed in claim 1 in which said means to superpose aDC voltage is adapted to superpose the DC voltage to thefrequency-divided output of the square-wave dividing circuit, and thecircuit includes means to set the DC voltage to be larger than twice thevoltage V between the base and the emitter of said buffer transistor,whereby the voltage V causes the bufi'er transistor to operate and thebuffer transistor is made conductive.

6. The circuit as in claim 2 which comprises a plurality of said stagesand means connecting them in cascade.

7. The circuit as in claim 3 which comprises a plurality of said stagesand means connecting them in cascade.

8. The circuit as in claim 4 which comprises a plurality of said stagesand means connecting them in cascade.

9. The circuit as in claim 5 which comprises a plurality of said stagesand means connecting them in cascade.

10. A circuit for producing signals of sawtooth wave, having one or morestages n," each comprising: a buffer transistor; at least two mixingresistors of equal value feeding at the base of the transistor an inputsawtooth wave and a square wave of equal peak amplitude; a frequencymixing circuit including said butter transistor and said resistors tomix the input sawtooth wave and square wave to produce a requiredsawtooth signal; a square-wave frequency-dividing circuit having anoutput thereof connected to one of said mixing resistors to feed saidsquare wave into the frequency-mixing circuit; and means including a DCvoltage source to make an emitter source voltage of said buffertransistor equal to or larger than 1 2 (1- n) VBE serving to start saidtransistor and, with the direction of said emitter source voltage setsuitably, maintain the transistor conductive.

1. A circuit for producing signals of sawtooth wave having at least onestage comprising: a buffer transistor; at least two mixing resistors ofequal value feeding at the base of the transistor an input sawtooth waveand a square wave of equal peak amplitude; a frequency mixing circuitincluding said buffer transistor and said resistors to mix the inputsawtooth wave and square wave to produce a required sawtooth signal; asquare-wave frequency-dividing circuit having an output thereofconnected to one of said mixing resistors to feed said square wave intothe frequency-mixing circuit; and means to superpose a DC voltage at aportion of the circuit so aS to lower ends of said divided frequencyoutput signal to an extent sufficient to compensate the voltage dropbetween the transistor base and emitter causing said buffer transistorto perform as a perfect class ''''A'''' amplifier.
 2. The circuit asclaimed in claim 1 which includes an emitter resistor connected at oneend thereof to the emitter of said buffer transistor the other end beingearthed, and a DC voltage superposing resistor connected between thebase and collector of the buffer transistor.
 3. The circuit as claimedin claim 1 in which said means to superpose a DC voltage is adapted tosuperpose the voltage in the same direction as the starting operationalvoltage of said buffer transistor.
 4. The circuit as claimed in claim 1in which said means to superpose a DC voltage includes connections tosuperpose the DC voltage to said input sawtooth wave, and means to setthe emitter source voltage of said buffer transistor to a value at leastequal to the DC voltage and to so set the direction of said emittersource voltage that the buffer transistor is conductive.
 5. The circuitas claimed in claim 1 in which said means to superpose a DC voltage isadapted to superpose the DC voltage to the frequency-divided output ofthe square-wave dividing circuit, and the circuit includes means to setthe DC voltage to be larger than twice the voltage VBE between the baseand the emitter of said buffer transistor, whereby the voltage VBEcauses the buffer transistor to operate and the buffer transistor ismade conductive.
 6. The circuit as in claim 2 which comprises aplurality of said stages and means connecting them in cascade.
 7. Thecircuit as in claim 3 which comprises a plurality of said stages andmeans connecting them in cascade.
 8. The circuit as in claim 4 whichcomprises a plurality of said stages and means connecting them incascade.
 9. The circuit as in claim 5 which comprises a plurality ofsaid stages and means connecting them in cascade.
 10. A circuit forproducing signals of sawtooth wave, having one or more stages ''''n,''''each comprising: a buffer transistor; at least two mixing resistors ofequal value feeding at the base of the transistor an input sawtooth waveand a square wave of equal peak amplitude; a frequency mixing circuitincluding said buffer transistor and said resistors to mix the inputsawtooth wave and square wave to produce a required sawtooth signal; asquare-wave frequency-dividing circuit having an output thereofconnected to one of said mixing resistors to feed said square wave intothe frequency-mixing circuit; and means including a DC voltage source tomake an emitter source voltage of said buffer transistor equal to orlarger than times the voltage VBE between the base and emitter of thebuffer transistor, said voltage serving to start said transistor and,with the direction of said emitter source voltage set suitably, maintainthe transistor conductive.